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At least 19 records

Equilibrium-gated pattern formation: How molecular dissociation thermodynamics drive emergent behavior in dissipative polymeric systems

Emergent patterns in biological systems arise through dissipative processes that balance reaction and transport phenomena, producing highly functional properties from self-regulating mechanisms. Synthetic fabrication, by contrast, often relies on user-controlled, multistep methods that lack the self-organizing capabilities of natural systems. Inspired by nature, we sought chemical systems that integrate strongly coupled reaction and transport phenomena, identifying frontal ring-opening metathesis polymerization (FROMP) as a method capable of creating diverse forms and functions through reactive processing. By employing discrete molecular initiators, FROMP allows precise control of key reaction steps—inhibition, initiation, and propagation. Using an integrated computational and experimental framework, we uncover how near-equilibrium inhibition dynamics, coupled with far-from-equilibrium reaction kinetics, drive pattern formation in frontally polymerized synthetic materials. We propose the concept of equilibrium-gated pattern formation, demonstrating how initiator chemistry can be tuned to achieve programmable macroscale properties. Our study reveals a surprising insight: Emergent behavior in FROMP systems arises from the inhibition-dominated regime of resin composition, expanding prior observations that such behavior is confined to a narrow compositional space near the boundary between front quenching and uniform front propagation. We identify a broader compositional window, far from the quenching regime, where emergent behavior reliably manifests. This expanded design space significantly enhances the operational flexibility of reactive systems and their capacity for self-organization. Furthermore, these insights provide a roadmap for designing bioinspired materials with self-organizing capabilities, unlocking possibilities in synthetic manufacturing.

Architected Polymers

3D pattern formation of a protein–membrane suspension

Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane, onto which they interact and form two-dimensional (2D) patterns. It is unclear how the membrane’s continuity and dimensionality impact pattern formation. Here, we address this gap using the MinDE system, a prototypical example of pattern-forming membrane proteins. We show that when the lipid substrate is fragmented into submicrometer-sized diffusive liposomes, adenosine triphosphate-driven protein–protein interactions generate three-dimensional (3D) spatially extended patterns, despite the complete loss of membrane continuity. Remarkably, these 3D patterns emerge at scales four orders of magnitude larger than the individual liposomes. By systematically varying protein concentration, liposome size, and density, we observed and characterized a variety of 3D dynamical patterns not seen on continuous 2D membranes, including traveling waves, dynamical spirals, and a coexistence phase. Simulations and linear stability analysis of a coarse-grained model revealed that the physical properties of the dispersed membrane effectively rescale both the protein–membrane binding rates and diffusion, two key parameters governing pattern formation and wavelength selection. These findings highlight the robustness of Min’s pattern-forming ability, suggesting that protein–membrane suspensions could serve as an adaptable template for studying out-of-equilibrium self-organization in 3D, beyond in vivo contexts.

36 MATERIALS SCIENCE

Efficient data-driven regression for reduced-order modeling of spatial pattern formation

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.

Data-driven modeling

Electrostatically driven pattern formation in mixed charged–neutral multicomponent elastic membranes

Multicomponent crystalline and amorphous elastic shells exhibit heterogeneous surface patterns that provide distinctive functionalities in cellular environments. Such patterning typically arises from the competition between short-range attractive and long-range repulsive interactions in membranes. Here, we demonstrate that the intrinsic competition between electrostatic repulsion and elastic deformation is sufficient to drive spontaneous surface patterning in elastic shells, requiring no additional attractive interactions. Using numerical simulations, we demonstrate pattern formation in mechanically homogeneous membranes with heterogeneous surface charge composition across different topologies, including spheres, discs, and flat periodic membranes. We also examine patterns in crystalline and amorphous shells of coassembled charged and neutral components with different bending rigidities. At low charge fraction, discrete charged surface domains form. At intermediate charge fraction, the competition between electrostatics and elasticity leads to elongated domains (rods) of the charged component, which results in lamellar patterns at nearly equal fraction of the charged and neutral components. At high charge fraction, nanodomains of the neutral component form. Amorphous shells exhibit similar progressions but with disordered structures rather than ordered lamellar patterns. These pattern morphologies are observed in both the closed shells and flat membranes. As salt concentration increases, all patterns coarsen due to the screening of electrostatic interactions.

charge heterogeneity

Subsurface Cooling and Sea Surface Temperature Pattern Formation Over the Equatorial Pacific

Abstract The equatorial cold tongue region has not warmed up in response to historical radiative forcing in the real world, contrary to the strong warming often simulated by climate models. Here we demonstrate that climate models fail to represent one or both of the key processes driving observed sea surface temperature (SST) pattern formation: a realistic surface wind stress pattern shaping subsurface cooling through wind‐driven circulation changes, and effective connectivity between subsurface and surface temperatures via upwelling and mixing. Consequently, none of the models approximate the observed lack of cold tongue SST warming and strengthening of zonal SST gradient across the equatorial Pacific. Furthermore, those that come closest achieve this due to interhemispheric warming differences rather than equatorial dynamics as observed. Addressing different origins of subsurface cooling in observations and simulations, and how they connect to SST, will lead to improved understanding of tropical Pacific SST changes to date and how they will evolve in the future.

Jiang, Feng [Lamont‐Doherty Earth Observatory Colu

Ratchet effects in cyclic pattern formation systems with competing interactions

Ratchet effects can appear for particles interacting with an asymmetric potential under ac driving or for a thermal system in which a substrate is periodically flashed. Here, we show that a different type of collective ratchet effect can arise for a pattern-forming system coupled to an asymmetric substrate when the interaction potential between the particles is periodically oscillated in order to cycle the system through different patterns. We consider particles with competing short-range attraction and long-range repulsion subjected to time-dependent oscillations of the ratio between the attractive and repulsive interaction terms, which causes the system to cycle periodically between crystal and bubble states. In the presence of the substrate, this system exhibits both a positive and a reversed ratchet effect, and we show that there is a maximum in the ratchet efficiency as a function of interaction strength, ac drive frequency, and particle density. In conclusion, our results could be realized for a variety of pattern-forming systems on asymmetric substrates where the pattern type or particle interactions can be oscillated.

36 MATERIALS SCIENCE

Probing the impact of oxygen negative ions on the self-organized pattern in 1 atm DC glow with liquid anode

In an atmospheric DC glow discharge with a liquid anode, the plasma anode glow attached to the grounded liquid surface under certain conditions self-organizes into coherent patterns. Optical emission spectroscopy revealed that the emission consists primarily of the second positive system of nitrogen, N 2 (C-B), whose excitation energy is low and sensitive to changes in the electron energy distribution. In addition to electrons, negative ions can accumulate in the anode sheath and affect the local space charge. It has been speculated that these negative ions play a role in pattern formation at the anode surface. In this work, the role of oxygen negative ions was explored. It was found that the formation of anode patterns requires at least a 7% volume fraction of oxygen in the ambient gas. Results showed that O 2 - is the dominant negative ion species in atmospheric DC glow discharge, with a density of ~10 12 cm -3 . While the presence of oxygen appears to be crucial for pattern formation, this study indicated that patterns still formed without geometric changes even when 62% of negative ions in the plasma were detached by a laser. This suggests that negative ions do not support the patterns, while oxygen's heating effect may induce instability at the anode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Morphogenesis of spin cycloids in a noncollinear antiferromagnet

Pattern formation in spin systems with continuous-rotational symmetry (CRS) provides a powerful platform to study emergent complex magnetic phases and topological defects in condensed-matter physics. However, its understanding and correlation with unconventional magnetic order along with high-resolution nanoscale imaging are challenging. Here, we employ scanning nitrogen vacancy (NV) magnetometry to unveil the morphogenesis of spin cycloids at both the local and global scales within a single ferroelectric domain of (111)-oriented BiFeO 3 , which is a noncollinear antiferromagnet, resulting in formation of a glassy labyrinthine pattern. We find that the domains of locally oriented cycloids are interconnected by an array of topological defects and exhibit isotropic energy landscape predicted by first-principles calculations. We propose that the CRS of spin-cycloid propagation directions within the (111) drives the formation of the labyrinthine pattern and the associated topological defects such as antiferromagnetic skyrmions. Unexpectedly, reversing the as-grown ferroelectric polarization from [$\overline{1}$ $\overline{1}$ $\overline{1}$] to [111] produces a noncycloidal NV image contrast which ¯ could be attributed to either the emergence of a uniformly magnetized state or a reversal of the cycloid polarity. These findings highlight that (111)-oriented BiFeO 3 is not only important for studying the fascinating subject of pattern formation but could also be utilized as an ideal platform for integrating novel topological defects in the field of antiferromagnetic spintronics.

magnetoelectric

Evaporation of a Reactive Nanofluid Sessile Drop: Capturing Rapid Emergence of Surface Crystals with In Situ Synchrotron X-ray Diffraction

Mechanisms for surface pattern formation from evaporation of a reactive nanofluid sessile drop are not well understood. In contrast to the coffee-ring effect from inert particles, rapid chemical and morphological transformation of reactive nanoparticles upon rapid evaporative drying are challenging to probe experimentally. Here, using grazing-incidence X-ray surface scattering, the nanostructure of nascent surface patterns has been probed as a ZnO nanofluid sessile drop rapidly dries. The high temporal resolution enabled by the high flux of synchrotron X-rays allows the observation of the emergence of Zn(OH) 2 surface crystals from the onset of evaporation and their rapid evolution into the final residual surface pattern, via transient layered complexes evident from the temporary appearance of X-ray diffraction peaks preceding Zn(OH) 2 formation. The results offer mechanistic insights of morphogenesis of surface patterns from evaporation-induced self-assembly and self-organization of reactive nanofluids, previously untenable using other experimental methods.

36 MATERIALS SCIENCE

Dynamic evolution of ultracold electron beams from nanostructured cathodes

Dynamic Coulomb expansion of dense, nonuniform particle beamlets can lead to causticlike formations in the charge density profile of the resultant beam. Such features only occur for cold beams where thermal diffusion of the particles is minimized. These phenomena have been observed experimentally for select cases with ion beams but not yet for electron beams as the electron dynamics occur over far faster timescales. We simulate the interaction of electron bunches while varying the initial transverse temperature and density profiles to determine the thresholds that characterize this pattern formation. Furthermore, we extend the simulations to geometric arrangements that are more pertinent to the nanotip cathode application and consider the effects of asymmetries and the impact of a low-density halo on the overall process. The simulations are conducted using a previously documented high-fidelity algorithm for collisional particle dynamics. These studies identify the temperature and density thresholds required for caustic formation and provide guidance for optimizing the design of nanoscale structured cathodes. We also demonstrate that the correlation between the final density patterns and the underlying beam parameters enables a virtual diagnostic tool for measuring ultralow emittance beams solely based on a transverse charge density profile.

43 PARTICLE ACCELERATORS

Emergence of complex-regular eutectic patterns in Al–Ge: Observations from correlative nano-imaging

Eutectic solidification exemplifies nonequilibrium pattern formation, making it a well-studied moving boundary problem. Yet the mechanisms behind the formation of complex-regular microstructures – particularly in highly anisotropic systems with a significant volume fraction of a faceted phase – remain poorly understood. Our understanding of such systems is made complicated by the nonlinear interface kinetics and unique growth dynamics characteristic of faceted phases. To address these challenges, we investigate a model Al–Ge eutectic system, where the faceted Ge phase constitutes a substantial volume fraction (~0.35) and where the two solid phases arrange into so-called “fishbone” or “feather” complex-regular patterns. Using synchrotron-based x-ray nano-imaging and nanotomography with high spatial resolution (22 nm per pixel), we capture in real-time the evolution of the solid–liquid interfaces and the resulting three-dimensional microstructures in this faceted/non-faceted eutectic system. By integrating these observations with electron backscattered diffraction, we elucidate the crystallographic biases on the solidification process and the mechanisms driving the formation of such complex-regular microstructures. These findings inform a new growth model for irregular eutectics in (near-)symmetrical phase diagrams, offering insight on advanced microstructural design and processing strategies. More broadly, we demonstrate how interfacial curvature is generated in irregular eutectic alloys and how it depends on the volume fraction of the faceted phase.

36 MATERIALS SCIENCE

Beyond the eutectic paradigm: nanolamellar patterns in a rapidly solidified peritectic alloy

Peritectic transformations are central to many structural alloys, yet pattern formation remains poorly understood due to complex growth dynamics and limited three-dimensional data. Here, we report an unusual two-phase microstructure in a Zn–Ag peritectic alloy subjected to rapid solidification by laser surface remelting. Synchrotron X-ray nanotomography reveals a lamellar structure of primary 𝜀-AgZn 3 and peritectic Zn with ∼700 nm spacing. Although resembling a eutectic morphology, this pattern forms without a eutectic reaction through non-steady coupled growth from the liquid. SEM and TEM-EDS confirm interface shapes and phase compositions. These findings expand the design space of peritectics for refined microstructural control.

36 MATERIALS SCIENCE

Explosive nucleation and growth of Pb islands on Ge(111) below room temperature via collective diffusion

Nucleation is a fundamental process in nature controlling phase transitions and pattern formation. Classical nucleation is based on the gradual aggregation of diffusing atoms after a critical cluster size is reached. Contrary to these expectations, we have observed in real time the formation of perfect Pb(111) islands with more than 10 5 atoms emerging out of the compressed wetting layer within a few seconds during growth of Pb on Ge(111) below room temperature. Pb deposited on Ge(111) in a temperature range between −30 °C and 10 °C exhibited explosive nucleation of height-selected islands upon reaching a critical coverage of 1.33 ± 0.07 ML with respect to Ge(111). Island nucleation was fueled by the 2% compression of the Pb wetting layer at the critical coverage. The island areas grew linearly with time, exhibiting collective diffusion, where thousands of atoms follow correlated, non-random walk diffusion. The total growth rate was higher with increasing temperature. Density functional theory simulations of the chemical potential and binding sites of the Pb/Ge(111) system give insight into the role of the compression of the wetting layer and the strain within the growing Pb layers, which explain this nonclassical behavior of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Phase-field model of freeze casting

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

Materials science

Echo state network for coarsening dynamics of charge density waves

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.

2-dimensional systems

Skyrmion-skyrmionium phase separation and laning transitions via spin-orbit torque currents

Many driven binary systems can exhibit laning transitions when the two species have different mobilities, such as colloidal particles with opposite charges in electric fields. Another example is pedestrian or active-matter systems, where particles moving in opposite directions form a phase-separated state that enhances the overall mobility. In this work, we use atomistic simulations to demonstrate that mixtures of skyrmions and skyrmioniums also exhibit pattern formation and laning transitions. Skyrmions move more slowly and at a finite skyrmion Hall angle compared to skyrmioniums, which move faster and without a skyrmion Hall effect. At low drives, the system forms a partially jammed phase where the skyrmioniums are dragged by the surrounding skyrmions, resulting in a finite angle of motion for the skyrmioniums. At higher drives, the system transitions into a laned state, but unlike colloidal systems, the lanes in the skyrmion-skyrmionium mixture are tilted relative to the driving direction due to the intrinsic skyrmion Hall angle. In the laned state, the skyrmionium angle of motion is reversed when it aligns with the tilted lane structure. At even higher drives, the skyrmioniums collapse into skyrmions. Below a critical skyrmion density, both textures can move independently with few collisions, but above this density, the laning state disappears entirely, and the system transitions to a skyrmion-only state. We map out the velocity and Hall responses of the different textures and identify three distinct phases: partially jammed, laned, and skyrmion-only moving crystal states. In conclusion, we compare our results to recent observations of tilted laning phases in pedestrian flows, where chiral symmetry breaking in the particle interactions leads to similar behavior.

36 MATERIALS SCIENCE

QPatLib v1.0 — Measurement-based quantum simulation Pauli string unitary pattern collections

This Zenodo record accompanies the paper “Scalable Measurement-Based Quantum Simulation Patterns for Benchmarking” arXiv.2605.12502 and provides QPatLib v1.0 measurement-pattern datasets in human-readable JSONL together with a ZIP archive of OpenQASM 3.0 circuits used for validation and reproducibility. The patterns and circuits implement Pauli string unitaries for benchmark cases. Cases include all possible string combinations for less than 6 qubits and strings used in Hamiltonians for certain diatomic molecules for 6 or more qubits. Format: Each pattern_*.jsonl file is containins measurement patterns for all subsets for a given model/instance and subset strategy: it begins with a preamble containing model metadata, subset definitions, provenance, and (when feasible) full-pattern test results, followed by one pattern entry per subset. Each subset entry includes a required pattern_ascii field storing the measurement pattern in the measurement-calculus/Graphix standard with signal shifting, written left-to-right in the canonical order nodes → edges → measurements (with signal dependencies) → byproduct corrections (X/Z). The circuits are included as circuit_files.zip. Patterns in this record were validated against the corresponding circuits and checked for causal flow. Codes for generating these patterns can be found at QPatLib repository on Github

Graphix

Directional locking and hysteresis in stripe- and bubble-forming systems on one-dimensional periodic substrates with a rotating drive

We examine the dynamics of a two-dimensional stripe, bubble, and crystal forming system interacting with a periodic one-dimensional substrate under an applied drive that is rotated with respect to the substrate periodicity direction 𝑥. We find that the stripes remain strongly directionally locked to the 𝑥 direction for an extended range of drives before undergoing motion parallel to the drive. In some cases, the stripes break apart at the unlocking transition, but they can dynamically reform into stripes aligned perpendicular to the 𝑥 direction, producing hysteresis in the directional locking and unlocking transitions. In contrast, moving anisotropic crystal and bubble phases exhibit weaker directional locking and reduced or no hysteresis. The hysteresis occurs in regimes where the particle rearrangements occur and is most pronounced near the stripe phase. In conclusion, we also show that for varied substrate strength, substrate spacing, and particle density, a number of novel dynamical patterns can form that include a combination of stripe, bubble, and crystal morphologies.

36 MATERIALS SCIENCE